Proyecciones
Vol. 22, N o 1, pp. 1-13, May 2003.
Universidad Católica del Norte
Antofagasta - Chile

NONRESONANCE BELOW THE SECOND
EIGENVALUE FOR A NONLINEAR
ELLIPTIC PROBLEM

M. MOUSSAOUI and M. MOUSSAOUI
University Mohamed I, Oujda, Morocco

Abstract

We study the solvability of the problem

when the nonlinearity g is assumed to lie asymptotically between 0 and the second eigenvalue ¸ We show that this problem is nonresonant.

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Received : May 2002.

M. MOUSSAOUI
Department of Mathematics
Faculty of Sciences
University Mohamed I
P. O. BOX 524
60000 Oujda
Morocco
e-mail : moussaoui@sciences.univ-oujda.ac.ma

and

M. MOUSSAOUI
Department of Mathematics
Faculty of Sciences
University Mohamed I
P. O. BOX 524
60000 Oujda
Morocco
e-mail : mimoun moussaoui@hotmail.com